# Thread: Quotient Rule

1. ## Quotient Rule

(A)(i) Use the Quotient Rule to differentiate the function
h(x) = 1 + In x (x > 0)
xxxxxxxxx

Please can somone help me before I pull my hair.
Thank you in advance

2. Originally Posted by omkara
(A)(i) Use the Quotient Rule to differentiate the function
h(x) = 1 + In x (x > 0)
xxxxxxxxx

Please can somone help me before I pull my hair.
Thank you in advance
I am unaware of what $In(x)$ is?

But I will assume the problem reads

$\frac{1+\color{red}{\ln(x)}}{x}$

In which case the quotient rule gives

$\frac{x\bigg(\frac{1}{x}\bigg)-(1+\ln(x))(1)}{x^2}$

Is that right?

3. Originally Posted by omkara
(A)(i) Use the Quotient Rule to differentiate the function
h(x) = 1 + In x (x > 0)
xxxxxxxxx

Please can somone help me before I pull my hair.
Thank you in advance
$h(x) = \frac{1 + ln x}{x}$

$h'(x) = \frac{(1 + ln x)'(x) - (x)'(1 + ln x)}{x^2}$

$h'(x) = \frac{(\frac{1}{x})(x) - (1)(1 + ln x)}{x^2}$

$h'(x) = \frac{(1 - (1 + ln x)}{x^2}$

$h'(x) = \frac{(-ln x)}{x^2}$